Unsupervised domain adaptation (UDA) intends to transfer knowledge from a labeled source domain to an unlabeled target domain. Many current methods focus on learning feature representations that are both discriminative for classification and invariant across domains by simultaneously optimizing domain alignment and classification tasks. However, these methods often overlook a crucial challenge: the inherent conflict between these two tasks during gradient-based optimization. In this paper, we delve into this issue and introduce two effective solutions known as Gradient Harmonization, including GH and GH++, to mitigate the conflict between domain alignment and classification tasks. GH operates by altering the gradient angle between different tasks from an obtuse angle to an acute angle, thus resolving the conflict and trade-offing the two tasks in a coordinated manner. Yet, this would cause both tasks to deviate from their original optimization directions. We thus further propose an improved version, GH++, which adjusts the gradient angle between tasks from an obtuse angle to a vertical angle. This not only eliminates the conflict but also minimizes deviation from the original gradient directions. Finally, for optimization convenience and efficiency, we evolve the gradient harmonization strategies into a dynamically weighted loss function using an integral operator on the harmonized gradient. Notably, GH/GH++ are orthogonal to UDA and can be seamlessly integrated into most existing UDA models. Theoretical insights and experimental analyses demonstrate that the proposed approaches not only enhance popular UDA baselines but also improve recent state-of-the-art models.

Federated learning (FL) is a privacy-preserving paradigm for collaboratively training a global model from decentralized clients. However, the performance of FL is hindered by non-independent and identically distributed (non-IID) data and device heterogeneity. In this work, we revisit this key challenge through the lens of gradient conflicts on the server side. Specifically, we first investigate the gradient conflict phenomenon among multiple clients and reveal that stronger heterogeneity leads to more severe gradient conflicts. To tackle this issue, we propose FedGH, a simple yet effective method that mitigates local drifts through Gradient Harmonization. This technique projects one gradient vector onto the orthogonal plane of the other within conflicting client pairs. Extensive experiments demonstrate that FedGH consistently enhances multiple state-of-the-art FL baselines across diverse benchmarks and non-IID scenarios. Notably, FedGH yields more significant improvements in scenarios with stronger heterogeneity. As a plug-and-play module, FedGH can be seamlessly integrated into any FL framework without requiring hyperparameter tuning.